2026-09-10T09:45:00Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:27721 2026-09-09T12:19:35Z ddc:004 open_access

Near-Optimal Streaming Approximation for Max-DICUT in Sublinear Space Using Two Passes Velusamy, Santhoshini Streaming algorithms Approximation algorithms Graph algorithms The Max-DICUT problem has emerged as a canonical problem for understanding the approximability of constraint satisfaction problems in the streaming model. A seminal result of Kapralov and Krachun [STOC 2019] shows that it is impossible to beat 1/2-approximation for Max-DICUT in sublinear space in the single-pass streaming setting, even on bounded-degree graphs. In a recent work, Saxena, Singer, Sudan, and Velusamy [SODA 2025] prove that the above lower bound is tight by giving a single-pass algorithm for bounded-degree graphs that achieves (1/2-ε)-approximation in sublinear space, for every constant ε > 0. For arbitrary graphs of unbounded degree, they give an O(1/ε)-pass O(log n) space algorithm. Their work left open the question of obtaining 1/2-approximation for arbitrary graphs in the single-pass setting in sublinear space. We make progress towards this question and give a two-pass algorithm that achieves (1/2-ε)-approximation in sublinear space, for every constant ε > 0. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Santhoshini Velusamy 2026 Is Part Of LIPIcs, Volume 392, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2026) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.APPROX/RANDOM.2026.4 urn:nbn:de:0030-drops-277211 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2026.4 eng https://creativecommons.org/licenses/by/4.0/legalcode